*The elder Free-Ride offspring conveys heartfelt thanks to those who provided quantum mechanical book recommendations in the comments on this post — and to Super Sally who sent three of those books as birthday presents. The elder offspring is about two chapters into Alice in Quantumland right now and pronounces it good. “There’s an electron bank, but the more energy you borrow, the faster you have to pay back the loan.”

*Since last week’s visual explanation of “why stone fruit has a butt-crack”, the Free-Ride offspring had another conversation in which the question of stone fruit intestines came up. (I’m pretty sure, although I could not prove it in a court of law, that this turn in the conversation was instigated by Dr. Free-Ride’s better half.) I had to point out that just as not every creature that has intestines has a butt-crack, so not every entity with a butt-crack has intestines.

I didn’t even need to resort to Venn diagrams.

*The younger Free-Ride offspring has been wondering who the first human was — because, you know, if there’s such a category as “human” there must have been a first individual that fulfilled that definition.

Younger offspring: Where did he come from?

Elder offspring: His parents. And the first human could have been a she.

Younger offspring: But if he was the first human, and his parents weren’t human, were they some kind of apes?

Dr. Free-Ride: Parents and their children never see totally eye to eye with each other.

Dr. Free-Ride’s better half tried to talk up the idea of first populations of humans rather than an individual first human. Then we started wondering if there are good kids books out there on the subject of the appearance of Homo sapiens on the evolutionary stage. (“Didn’t we read some book about early humans?” asked Dr. Free-Ride’s better half. Yes, but it seemed more focused on the products of cultural evolution, and it was self-consciously anachronistic.)

Recommendations?

*From the Free-Ride gene-splicing laboratory, there have been preliminary discussion of developing hybrids from bees and geese. The advantage: honey-filled eggs. The disadvantage: the honking before they sting you.

Younger Offspring makes an important point. We’re socialized to divide the world into discrete parts, but hardly anything in the natural world is discrete. YO’s example, more generally, was why (too long ago) I proposed what were later called fuzzy sets. Homo sapiens, like other species, constitutes a fuzzy set, one that has no precise demarcation from its ancestor. So there never was a first human, but populations that gradually became more (and probably sometimes less) human.

It sounds like the sprogs might appreciate the Paradox of the Heap . If we have a heap of sand, and remove a grain of sand from it, we still have a heap of sand. But one grain of sand is not a heap. If we keep removing grains from a heap, at what point does it stop being a heap of sand?

That and the Zeno paradoxes fascinated me as a child. My sister was less impressed. When I explained the Paradox of the Heap to her, she blithely answered “twelve grains.” Siblings can be infuriating like that sometimes.